Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 1 - Functions - 1.1 Review of Functions - 1.1 Exercises - Page 10: 14

Answer

Domain: (-$\infty$, -2) U (-2, 3) U (3, $\infty$) Range: (-$\infty$, $\infty$)

Work Step by Step

In order to achieve the domain, the denominator cannot be equal to 0, so solve: 0$\ne$(y+2)(y-3) y+2$\ne$0 y$\ne$-2 y-3$\ne$0 y$\ne$3 Set into interval notation these values make: (-$\infty$, -2) U (-2, 3) U (3, $\infty$) To find the range, it can be observed from the graph that the lines extend upwards and downwards continuously, therefore, the range is (-$\infty$, $\infty$)
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